Question

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Answer 1

?

Answer 2

why isn't it
\[20!\]?

Answer 3

oh i see why never mind

Answer 4

1745944200, though it seems awfully large

Answer 5

I was thinking about it backwards

Answer 6

see http://www2.wolframalpha.com/input/?i=lcm%282%2C4%2C6%2C8%2C10%2C12%2C14%2C16%2C18%2C20%2C22%2C24%2C26%2C28%2C30%2C32%2C34%2C36%2C38%2C40%29

Answer 7

its\[2^4\cdot3^2\cdot5\cdot7\cdot11\cdot13\cdot17\cdot19\]

Answer 8

\[20! = 2.43290200817664 × 10^18\]

Answer 9

232792560

Answer 10

ok you know you need
\[2,3,5,7,13,17,19\] as factors, now lets see what powers you need.
need
\[2^4\] to get 16
need
\[3^2\] to get 9, and i think that is it because
\[5^2=25\] too big, so i am going to say
\[2^4\times 3^2\times 5\times7\times 13\times 17\times 19\]

Answer 11

dont forget 11 satellite :)

Answer 12

aaaand joemath hits the jackpot.

Answer 13

i will let joemath correct me if i am wrong.

Answer 14

\[2^4\times 3^2\times 5\times7\times 11\times 13\times 17\times 19\]

Answer 15

forgot one didn't i

Answer 16

the idea was right though. just look and see what powers of primes are included from 1 to 20.

Answer 17

oh wow i didn't see you had the answer miles above...

Answer 18

no one see's my posts =/ lolol jk

Answer 19

@across - I thought you said "evenly divisible"?

232792560 / 17 = 14549535
which is not an even number?

Answer 20

I missed the powers of primes part :(

Answer 21

by evenly divisible, i understood it as "no remainder"

Answer 22

That's how I took it

Answer 23

sorry I meant 232792560 / 16 = 14549535

Answer 24

Even divisibility often implies a division leaving no remainder.

Answer 25

ok - my misunderstanding then.